Questions tagged [topology]
In mathematics, topology examines the properties of space (such as connectedness and compactness) that are preserved under continuous deformations, such as stretching and bending, but not tearing or gluing.
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Is it possible to use topology arguments to find analogies in thermodynamic systems?
I was contemplating whether, given the mathematical structure of thermodynamics, it might be possible to restate some of its most important propositions—or even all of them—purely in topological terms....
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Topology of the valence Bloch bundle for a $d = 2$ Chern insulator
I am currently working on topological insulators, and I'm reading the review An introduction to topological insulators by Carpentier and Fruchart. In this review, they use the fiber bundle language to ...
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Can one encode topology into the position operator in quantum mechanics?
We work with the concrete example of electromagnetism, but we intend to ask a question in broader scope at the end.
In classical field theory, the electromagnetic potential $\mathcal{A}$ lives on a ...
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Why in the Aharonov-Bohm effect the fact that the space is not simply connected leads to a vector potencial circulation different to zero?
I don't understand it, I don't know much about college mathematics, but why does the vector potential have to be constant if there is no hole in space but can have different values if there is a hole ...
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When dealing with a space like $AdS_5$, why can we take the universal cover?
In the context of the AdS/CFT correspondance, when considering $AdS_5$ we can pick the coordinates
$$x_0=R\:cosh(\rho)\: cos(\tau)
\\ x_5=R\:cosh(\rho)\:sin(\tau)
\\ x_i=R\:sinh(\rho)\:\hat{x}_i,\;\;\;...
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How does Newtonian gravity work in a toroidal universe?
Suppose that the universe is not isotropic, so we can fix directions $x,y,z$. Furthermore, suppose there are periodic boundary conditions such that we identify $x\sim x+L$ and $y\sim y+L$ (similar to ...
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Global Hyperbolicity of Spacetimes implying Connectedness
I am currently working on a problem and right now I want to show that the global hyperbolicity of a spacetime M implies, that M is connected. Therefore, I assumed the following:
We could write $M$ as ...
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Are de Sitter, Anti-de Sitter and Minkowski spaces spatially infinite?
I am not someone who has studied general relativity, however have recently developed an interest in it. From what I have seen online, de Sitter, Minkowski and Anti-de Sitter spaces are often compared ...
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Are there closed simply connected 2D manifolds that do not require a third dimension?
In the context of cosmology, space is commonly described as potentially having a global curvature that can be positive, zero, or negative. A common way that textbooks describe positive curvature is by ...
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Can part of space be causally disconnected from the rest of the universe by being surrounded by black holes? [duplicate]
Is it possible for black hole event horizons to overlap and form a spherical wall around an island of space (that's not inside a black hole) while still being causally disconnected from the rest of ...
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Instantons in the Global $O(2)$ Model (Compact scalar field) - Polyakov textbook
This question is related with Polyakov, "Gauge Fields and Strings" section 4.2
In section 4.2, partition function is
\begin{equation}
Z=\sum_{n_{x,\delta}}\int_{-\pi}^{\pi}\prod_x\frac{d\...
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Action principle dependent on spacetime-topology?
Consider the Lagrangian density
$$L(\phi, \nabla \phi, g) = g^{\mu \nu} \nabla_{\mu} \phi \nabla_{\nu} \phi$$
If one varies the action as usual, then one finds the equation
$$\delta S = \int_{\mathcal{...
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What is the importance of $SU(2)$ being the double cover of $SO(3)$?
To my understanding, it is important that $SU(2)$ is (isomorphic to) the universal cover of $SO(3)$. This is important because $SU(2)$ is then simply-connected and has a Lie algebra isomorphic to $\...
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The topology of planets [duplicate]
Just a curiosity:
Let $g \in \mathbb{Z}_{>0}$. Is it possible for a planet of topological genus $g$ to exist? For example, is there any contradiction (from the point of view of physics) in assuming ...
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What is the topology of a spacelike cross-section of a null hypersurface?
I'm studying the peeling-off behaviour of zero rest-mass fields, as described in Penrose's paper. In it, he talks about the boundary $\mathscr{I}$ of the conformal completion of an asymptotically ...
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